just to give a different point of view, I've followed a routine with my DS since birth nearly, he is now 14 weeks and very well fed and happy...
at 7 weeks I was feeding him at 7,am, 10 am, bit more at 11.30, again at 2pm, 5pm, 6.30 pm, waking him to feed at 10.30 pm then waiting in the night till he woke hungry, usually about 3-4 am. I made sure he had really had enough and wasn't too sleepy to feed properly, and he was really really happy on this routine, so that i knew when he was and wasn't hungry so knew to look for other reasons why he might cry (usually tiredness). He literally only cries about 20 mins total per day, and I really think it's because of having a set routine with larger feeds. Of course it's important to keep your supply going, but I found it fine as your breasts get such a workout during growth spurts.
Of course, if he seemed hungry I would feed at whatever time, but I genuinely think at least for my DS he was happier having a good 'stuff' every 3 hours.. the trouble with feeding on demand is that sometimes food is not what the baby wants,
best of luck!